NEW YORK — Starting this week, you could own a piece of the Empire State Building.

Or, if iconic New York skyscrapers aren’t your thing, you could bite into Potbelly, a sandwich chain with more than 280 shops.

During the week, these and two more companies with familiar names — the owner of budget-friendly clothing store chain Burlington Coat Factory and Re/Max, one of the country’s largest real estate agencies — are expected to sell shares in initial public offerings.

A surging stock market is drawing investors to IPOs. In the past week, 12 companies went public. That’s the most in one week since November 2007, said data provider Dealogic. And there have been 151 IPOs in the United States this year, up 47 percent from a year ago, said IPO research firm Renaissance Capital.